Posted by **Kayleigh** on Wednesday, April 10, 2013 at 12:03pm.

Consider the functions

f(x)= 5x+4/x+3(This is a fraction) and

g(x)= 3x-4/5-x(This is a fraction)

a)Find f(g(x))

b)Find g(f(x))

c)Determine whether the functions f and g are inverses of each other.

- Consider the functions -
**Steve**, Wednesday, April 10, 2013 at 12:37pm
f(g) = (5g+4)/(g+3)

= (5(3x-4)/(5-x)+4) / ((3x-4)/(5-x)+3)

= x

g(f) = (3f-4)/(5-f)

= (3((5x+4)/(x+3))-4) / (5-((5x+4)/(x+3)))

= x

since f(g) = g(f) = x, they are inverses

- Consider the functions -
**Kayleigh**, Wednesday, April 10, 2013 at 12:44pm
What are the values that need to be excluded?

- Consider the functions -
**Steve**, Wednesday, April 10, 2013 at 12:53pm
whatever makes the denominator zero must be excluded, since division by zero is undefined.

So, for f(g), x=5 is not allowed, since g(5) is not defined. In addition, since f(-3) is not defined, any x where g(x) = -3 must also be excluded. Luckily, there is no such x.

Use similar reasoning for g(f).

- Consider the functions -
**Kayleigh**, Wednesday, April 10, 2013 at 12:56pm
So there are no values to be excluded?

- Consider the functions -
**Steve**, Wednesday, April 10, 2013 at 1:04pm
Read what I said. You have to exclude x=5 because g(5) is not defined. Therefore, f(g(5)) is also not defined.

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